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| radian per second | |
|---|---|
 | |
| General information | |
| Unit system | SI |
| Unit of | angular speed |
| Symbol | rad/s, rad⋅s−1 |
Theradian per second (symbol:rad⋅s−1 orrad/s) is the unit ofangular velocity in theInternational System of Units (SI). Theradian persecond is also the SI unit ofangular frequency (symbolω, omega). The radian per second is defined as the angular frequency that results in theangular displacement increasing by one radian every second.[1]
Afrequency of onehertz (1 Hz), or onecycle per second (1 cps), corresponds to an angular frequency of 2π radians per second. This is because onecycle of rotation corresponds to anangular rotation of 2π radians.[2]
Since the radian is adimensionless unit in theSI, the radian per second is dimensionally equivalent to the hertz—both can be expressed asreciprocal seconds, s−1. So, context is necessary to specify whichkind of quantity is being expressed, angular frequency or ordinary frequency.
One radian per second also corresponds to about 9.55revolutions per minute (rpm).[3]Degrees per second may also be defined, based ondegree of arc, where 1 degree per second (°/s) is equivalent toπ/180 rad⋅s−1.
| Angular frequency | Frequency |
|---|---|
| 2π rad/s | 1 Hz |
| 1 rad/s | ≈ 0.159155 Hz |
| 1 rad/s | ≈ 9.5493 rpm |
| 0.1047 rad/s | ≈ 1 rpm |
A use of the unit radian per second is in calculation of the power transmitted by a shaft. In theInternational System of Quantities (SI) and theInternational System of Units, widely used inphysics andengineering, the powerp is equal to the angular speedω multiplied by thetorqueτ applied to the shaft:p =ω ⋅τ. Whencoherent units are used for these quantities, which are respectively thewatt, the radian per second, and thenewton-metre, and thusW = rad/s ×N·m, no numerical factor is needed when performing the numerical calculation. When the units are not coherent (e.g.horsepower,turn/min, andpound-foot), an additional factor will generally be necessary.
